On a multipoint nonlocal initial value problem for a singularly-perturbed first-order ODE by Dovlet M. Dovletov

“…The existence of a classical solution of the multipoint nonlocal initial value problem (NLIVP) is proved. …”
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The Half-Space Sommerfeld Problem of a Horizontal Dipole for Magnetic Media by Seil Sautbekov, Merey Sautbekova

“…An integral representation of the exact expression for the Hertz potential, which generalizes the classical solution for non-magnetic media, both in cylindrical and spherical coordinate systems, is obtained. …”
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Local Well-Posedness and Blow-Up for the Solutions to the Axisymmetric Inviscid Hall-MHD Equations by Eunji Jeong, Junha Kim, Jihoon Lee

“…Second, we consider the inviscid axisymmetric Hall equations without fluids and prove that there exists a finite time blow-up of a classical solution due to the Hall term. Finally, we obtain some blow-up criteria for the axisymmetric resistive and inviscid Hall-MHD equations.…”
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Magnetic Monopoles in Multivector Boson Theories by Koichiro Kobayashi, Nahomi Kan, Kiyoshi Shiraishi

“…A classical solution for a magnetic monopole is found in a specific multivector boson theory. …”
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Asymptotic Behavior of an Optimal Investment-Reinsurance Problem with General Utility Functions by Yan Zhang, Peibiao Zhao

“…By solving the solution to the dual HJB equation, we derive a classical solution to the primal HJB equation and obtain the expression of the optimal investment-reinsurance strategy, then some examples, which would be difficult to solve with the standard method, are given to demonstrate the usefulness of our dual control method. …”
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BENDING VIBRATION CHARACTERISTICS ANALYSIS OF THE CONVEYOR BELT WITH THE STEEL ROPE CORE BASED ON THE ORTHOGONAL ANISOTROPY SHEET MODEL by CHEN HongYue, LI EnDong, ZHANG Kun, MAO Jun, BAI YangXi, MA Ying

“…The transverse free vibration model of the rubber conveyor belt with the steel rope core is established based the small deflection theory of the orthogonal anisotropy sheet model. By using the classical solution method, the analytical solutions of the SFSF boundary model of the lower branch conveyor belt, the SCSC boundary model of the upper branch slot shape bottom, and the SFSC boundary model of the side. …”
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Efficient i-DFA construction algorithm based on state grouping by Deng-ke QIAO, Qing WANG, Ting-wen LIU, Yong SUN, Li GUO

“…Regular expression matching plays an important role in many network and security applications.DFA is the preferred representation to perform regular expression matching in high-speed network,because of its high and stable matching efficiency.However,DFA may experience state explosion,and thus consume huge memory space.As a classical solution for the problem of state explosion,i-DFA can reduce the memory consumption significantly and guarantee the worst matching performance at the same time.However,prior methods are inefficient in both time and space during the construction of i-DFA.An efficient i-DFA construction algorithm based on the idea of state grouping was proposed.Furthermore,a formal description for the problem of state grouping was given,and it was proved that it was NP-hard to get the best state grouping result.Thus,based on local search strategy,a near-optimal algorithm was introduced to divide states into different groups.Compared with the classical construction method,the significant improvement in both time and space is achieved; the i-DFA of the proposed method may have 2/3 states as that of prior method and the proposed i-DFA is constructed with only 1/16 time of it.…”
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Global boundedness of solutions to a chemotaxis consumption model with signal dependent motility and logistic source by Baghaei, Khadijeh

“…$For the above system, we prove that the corresponding initial boundary value problem admits a unique global classical solution which is uniformly-in-time bounded. This result is obtained under some conditions on initial value $ v_{0}$ and $\mu $ and without any restriction on $k$ and $\alpha .$ The obtained result extends the recent results obtained for this problem.…”
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Shake Table Study on the Efficiency of Seismic Base Isolation Using Natural Stone Pebbles by Ivan Banović, Jure Radnić, Nikola Grgić

“…., the reduction in the seismic forces and stresses in the structure compared to the classical solution of foundation, significantly depends on the type of the applied excitation and depends relatively little on the layer thickness and pebble fraction. …”
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Vibrational Energy Flow Analysis of Corrected Flexural Waves in Timoshenko Beam – Part I: Theory of an Energetic Model by Young-Ho Park, Suk-Yoon Hong

“…The results obtained by the derived energy flow model for simple finite Timoshenko beams are compared with those of the classical solutions for the Timoshenko beam, the energy flow solution, and the classical solution for the Euler-Bernoulli beam with various excitation frequencies and damping loss factors of the beam. …”
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Revisiting classical concepts of Linear Elastic Fracture Mechanics - Part I: The closing �mathematical� crack in an infinite plate and the respective Stress Intensity Factors by Christos F. Markides, Stavros K. Kourkoulis

“…The motive of this first paper is to highlight some controversial issues, related to the unnatural overlapping of the lips of a �mathematical� crack in an infinite plate loaded by specific combinations of principal stresses at infinity (predicted by the classical solution of the respective first fundamental problem), and the closely associated issue of negative mode-I Stress Intensity Factor. …”
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Boundedness and large time behavior of a signal-dependent motility system with nonlinear indirect signal production by Ya Tian, Jing Luo

“…We show that if $ {\frac{l}{\beta}} > {\frac{n}{2}} $, the system has a unique global classical solution. Moreover, the solution exponentially converges to $ ((\frac{r} {\mu})^{\frac{1}{l-1}}, (\frac{1}{\delta})^{\beta}(\frac{r}{\mu})^{\frac{\beta}{l-1}}, \frac{1}{\delta}(\frac{r}{\mu})^{\frac{1}{l-1}})) $ in the large time limit under some extra hypotheses.…”
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Resurgence in Liouville theory by Nathan Benjamin, Scott Collier, Alexander Maloney, Viraj Meruliya

“…Here we investigate the nature of the perturbative expansion in powers of ℏ, which is the loop expansion around a semi-classical solution. We show that the perturbative coefficients grow factorially, as expected of a Feynman diagram expansion, and take the form of an asymptotic series. …”
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Global boundedness in a Keller-Segel system with nonlinear indirect signal consumption mechanism by Zihan Zheng, Juan Wang, Liming Cai

“…. $ It has been proven that if $ r_{1} > 2r_{2}+1, $ then the problem admits a global and bounded classical solution for some appropriate nonnegative initial data.…”
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An adaptive least-squares algorithm for the elliptic Monge–Ampère equation by Caboussat, Alexandre, Gourzoulidis, Dimitrios, Picasso, Marco

“…The results of numerical experiments support the convergence of our relaxation method to a convex classical solution, if such a solution exists. Otherwise they support convergence to a generalized solution in a least-squares sense. …”
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Analysis of global dynamics in an attraction-repulsion model with nonlinear indirect signal and logistic source by Chang-Jian Wang, Jia-Yue Zhu

“…. $ In this paper, we showed that if either $ \kappa_{1}\kappa_{2} < \max\{\frac{2}{n}, \kappa_{3}, \kappa-1\} $ or $ \kappa_{1}\kappa_{2} = \max\{\frac{2}{n}, \kappa_{3}, \kappa-1\} $ with the coefficients and initial data satisfying appropriate conditions, then the system possessed a global classical solution. Furthermore, we also have studied the convergence of solutions to a special case of the above system with $ \kappa = \delta+1, \kappa_{1} = 1, \kappa_{2} = \kappa_{3} = \delta $ for $ \delta > 0. $ It has been proven that if $ \mu > 0 $ is large enough, then the corresponding classical solutions exponentially converged to $ ((\frac{\lambda}{\mu})^{\frac{1}{\delta}}, \frac{\lambda}{\mu}, \frac{\lambda}{\mu}, \frac{\lambda}{\mu}), $ where the convergence rate could be formally expressed by the parameters of the system.…”
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A note on the global existence and boundedness of an N-dimensional parabolic-elliptic predator-prey system with indirect pursuit-evasion interaction by Liu Ling

“…Under appropriate conditions, utilizing suitable a priori estimates, we demonstrate that if (N−2)+N<max(r1−1)(r2−1),4N2,(r1−1)2N,(r2−1)2N\frac{{\left(N-2)}_{+}}{N}\lt \max \left\{\phantom{\rule[-0.95em]{}{0ex}},\left({r}_{1}-1)\left({r}_{2}-1),\frac{4}{{N}^{2}},\left({r}_{1}-1)\frac{2}{N},\left({r}_{2}-1)\frac{2}{N}\right\}, then the system admits a unique, uniformly bounded global classical solution. This finding extends the results of several previous studies.…”
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Semilinear Volterra Integrodifferential Problems with Fractional Derivatives in the Nonlinearities by Mokhtar Kirane, Milan Medveď, Nasser-eddine Tatar

“…We prove existence and uniqueness of mild solutions and classical solutions in appropriate spaces.…”
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On an Inverse Boundary Value Problem for a Fourth Order Elliptic Equation with Integral Condition by Yashar T. Mehraliyev

“…Further, using these facts, the existence and uniqueness of the classic solution of the initial problem are proved.…”
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Remarks on quasilinear evolutions equations by James E. Munoz Rivera

“…In this paper we study the existence result of classical solutions for the quasilinear equation utt−Δu−M(∫Ω|∇u|2dx)Δutt=f, with initial data u(0)=u0, u(1)=u1 and homogeneous boundary conditions.…”
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